Question: Rewrite as a simplified fraction. ${0.40\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 407.7777...\\ 100x &= 40.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 367}$ ${x = \dfrac{367}{900}} $